### INSTRUMENTS AND SYSTEMS OF AUTOMATIC CONTROL

METHOD OF CONTROL OVER SPACECRAFT CONVERGENCE WITH ORBITAL OBJECT DURING LONG-RANGE GUIDANCE
Avksentyev Alexander A.

689

A method of control over spacecraft during its long-range convergence with orbital object is considered. Angular movement dynamics of the spacecraft with a jet engine rigidly fixed on its body is taken into account. The current control action is calculated with consideration for the influence of noncentral gravitational field, the piecewise continuous jet engine operation, and restrictions on characteristic velocity. Values of equivalent coplanar motion parameters of the spacecraft used for calculations are predicted for the time of passage of the opposite point of the line of apsides. Results of computer simulations are presented to confirm the efficiency of the algorithms developed using the proposed method.

EFFECT OF NONLINEAR CONTROL ON RESONANCE IN A SELF-OSCILLATING ACCELEROMETER
Karpikov Stanislav R., Skalon Anatoly I.

697

Approaches to the problem of increasing accelerometer bandwidth is considered as one of the main characteristics of the device defining the area of its application. A method for increasing the bandwidth together with an increase in the resonance frequency of the accelerometer sensing element using non-linear self-oscillating control law is proposed. The bandwidth assessment is based on computer simulation of the frequency response characteristics of eleven variants of linear acceleration sensor designs, with three of them operating in the forced oscillation mode and five in the self-oscillation mode. The applied model uses two- and three-point relay control laws with hysteresis. For the design variants under
consideration, replacement of linear control loop by a non-linear one, enables the bandwidth expansion up to eight times by increasing the oscillation frequency without changing the mechanical properties of the sensor.

TRAJECTORY CONTROL OF SOLID BODY SPATIAL MOTION
Wang Jian , Kapitanyuk Yuri A, Chepinsky Sergey A, Холунин С. А., Denis A. Khvostov, Krasnov Aleksander Yu., Yifan Chen, Huimin Liu

704

The problem of synthesis of the trajectory control algorithm for a solid body moving with a preassigned speed along a spatial trajectory given in an implicit form, is considered. The control law is synthesized using differential geometry methods through the nonlinear transformation of the initial dynamic model. Effectiveness of the proposed mathematical model of spatial motion and corresponding nonlinear control algorithm is confirmed by presented results of computer simulation. The formulated control laws is supposed to be useful in development of systems of trajectory control over airborne and underwater mobile robots.

### COMPUTER TECHNIQUE

APPLICATION OF SEVERAL WAVELETS FOR GENERATING WIDEBAND SIGNALS
Grishentsev Alexey Yu., Korobeynikov Anatoliy Grigorievich

712

Signal synthesis with the use of a family of b-spline wavelets and Morley wavelets is analyzed on the base of complex-valued matrices with a special form of the autocorrelation function. The limits of applicability of the method for broadband signal synthesis using wavelet functions are Investigated. Conditions on wavelets suitable for synthesis of wideband signals based on complex-valued matrices are formulated. Statistical selection of wavelet used as the base for synthesized signals providing the best form of the autocorrelation function is carried out. Criteria and parameters of the wavelet formation for wideband signals synthesis are presented. The possibility of application of a family of b-spline wavelets and Morley wavelets is established for the case when an effective control of the spectrum of the broadband signal is required. It is shown that application of wavelets for synthesis of sub-noise wideband signals at a fixed frequency-time resource is inappropriate due to substantial nonuniformity of the signal energy distribution.

APPLICATION OF ALFREY'S FORMULA IN THE THEORY OF RANDOM PROCESSES
Vladimir A. Smagin , Igor А. Karabelnikov, Petrova Irina S.

721

An approximate method using Alfrey’s formula is proposed for derivation of digital values of function with image represented by a complex Laplace transform. The formula was obtained in the study of mechanical properties of high polymers; it is based on filtering the integrand of Laplace transform with the delta-function. A solution of an integral equations with temporal redundancy for the probability of task execution by a system is presented as an example. Attempts to improve the accuracy of the inverse transformation using the mathematical apparatus of Haar’s or Widder’s methods are reported to be unsuccessful.

### GYROSCOPIC AND NAVIGATION SYSTEMS

METHOD FOR ELASTIC STRAIN VERIFICATION IN FIBER-OPTIC GYROSCOPE CIRCUIT
Esipenko Ivan A., Lykov Daniil A.

728

The influence of elastic strain on variation of light wave phase in a fiber-optic gyroscope is studied both numerically and experimentally. Solution to the stationary thermos-elasticity problem for a structurally inhomogeneous fiber circuit is derived to determine local elastic strains in the fiber. The temperature effect on the object under investigation is taken as a load. The numerical solution to the problem is found out by the finite element method in the ANSYS software. Calculated distributions of elastic strain along the fiber are presented. The frequencies of stimulated Brillouin scattering at two temperatures are determined experimentally using an optical time domain analyzer. The influence of temperature variations and elastic strain on the Brillouin frequency shift is established. The calculated strain values are shown to be in accordance with the experimental data.

ANALYTICAL STUDY OF ACCURACY OF SPACE ROBOT NAVIGATION BY JOINT ONBOARD MEASUREMENTS OF ANGULAR AND LINEAR PARAMETERS OF AN ORBITAL OBJECT MOTION
Golyakov Alexey D., Ivan V. Fominov, Korolev Stepan Yu.

734

Analytic expressions describing. The accuracy of determination of motion parameters of mass center of a space robot flying at a relatively short distance from a passive orbital object is considered. The investigation is based on the theory of analytical assessment of autonomous navigation system accuracy, and accounts for simultaneous measurements of angular and linear navigation parameters carried out with ground and onboard measuring means. The calculations performed on the example of primary navigation parameters measured by astronomical angle meter and a rangefinder are presented. The results demonstrate that the measuring means assure determination of all the parameters characterizing the movement of the space robot mass. The resulting covariance matrix of the errors of the robot navigation derived in analytic form, make it possible to form the complex of the robot measuring means at the stage of substantiation of its technical appearance.

### INSTRUMENTS OF PRECISION MECHANICS

APPLICATION OF THREE-RIBBON ELASTIC SUPPORT WITH QUASI-ZERO REACTIVE TORQUE IN TEST BENCHES
Vetrenko Vladimir I.

742

A three-band elastic support with adjustable opposing torque and adjustable alignment of rotation elements is presented. The design of the support allows to provide quasi-zero reactive moment at small deviation angles. It is noted that the lack of universal formulas for calculation of the support complicates calculation of its geometrical sizes. Methods of the theory of elasticity are used to derive formulas for torsional, axial, and radial stiffness of the support using generalized Hooke's law. The analytical expressions of the generalized reactions of elastic elements and formulas to calculate the stiffness of the support are developed. A suspension with six elastic bands equipped with devices that create tension force compression and simultaneously performs the function of regulating the alignment of rotating elements, is used for experimental verification of the formulas. The experimental results fully confirmed the main theoretical insights. It is supposed that the obtained expressions can be used when creating elastic suspensions in precise instrumentation.

### OPTICAL AND OPTO-ELECTRONIC INSTRUMENTS AND SYSTEMS

METHOD OF DOUBLE CROSSED DISPERSION
Panchuk Vladimir E., Klochkova Valentina G., Yushkin Maxim V., Sendzikas Eugeny G., Marchenko Danil V.

753

Observations of stars with spectral resolution R=λ/δλ>200000 are reported to provide an opportunity to explore new effects and phenomena in stellar atmospheres, circumstellar shells and the interstellar medium. Several astrophysical problems requiring the observations with the spectral resolution of R≥200000 are reviewed briefly. Increasing spectral resolution necessitates collection of additional light, i.e., application of a telescope of large diameter. The value of the spectral resolution of a prism or a diffraction spectrograph is directly proportional to the diameter d of the collimated beam in the spectrograph and inversely proportional to the telescope diameter D. The dimensions of the ruled diffraction gratings with profiled grooves has reached their technological limits, so the potential for increasing d is exhausted. The use of a Fabry-Perot interferometer (FPI) in combination with a diffraction spectrograph is supposed to provide a perspective solution to the problem of registering stellar spectra with high and ultra-high-resolution. To increase the number of simultaneously registered spectral elements, a scheme including a spectrograph with crossed dispersion (an echelle spectrograph) used for the spatial separating orders of a FPI is considered. The approach is denoted as the method of double-crossed dispersion (DCD). Some problems of technical implementation and application of the DCD method at the 6-meter telescope BTA are discussed. Mathematical processing of the signal is also considered.

ANALYTICAL CONDITION OF CORRECTING SPHERICAL ABERRATION IN THE LENS WITH AXIAL INHOMOGENEITY OF THE REFRACTIVE INDEX
Alexander L. Sushkov, Gusev Sergey А.

764

Axial distribution of the refractive index in glass lens is proposed as a mean for correction of spherical aberration. The function describing the refractive index distribution along the lens surface to correct the spherical aberration is derived for the case of remote object imaging at various relative aperture values. Angular coefficient of inclination of the axial distribution of refractive index is shown to be the decisive factor when correcting spherical aberration. The use of gradient media is supposed to be promising in the manufacture of optical elements with best light-transmission characteristics.

### SCIENTIFIC AND PRACTICAL DEVELOPMENTS

METHOD OF AUTONOMOUS IDENTIFICATION OF CONVERSION FACTOR OF PENDULUM COMPENSATING ACCELEROMETER ON THE BASIS OF A REFERENCE MODEL
Ivan V. Fominov, Andrey N. Maletin, Klychnikov Alexey I.

770

The actual task of testing metrological characteristics of measuring devices incorporated into spacecraft control system during orbital flight is considered. The task is performed on the example of a pendulum accelerometer of the compensation type. Test actions on the feedback circuit of the accelerometer are developed, the transient characteristic of the corresponding response signals of the accelerometer are analyzed. The developed method of autonomous indirect identification of the conversion factor of pendulous compensating accelerometer is based on an iterative procedure of refinement of the reference model, and is characterized by the use of analytical expressions for the transition process under test actions. Numerical results are presented to confirm that the proposed method allows for highly accurate determination of the changing conversion factor for compensating accelerometer in conditions of orbital flight by built-in hardware and software means.

STUDY OF DYNAMIC ELECTROPHYSICAL CHARACTERISTICS OF SUNFLOWER OILS OF VARIOUS COMPOSITION
Lukyanov Gennadiy N, Kowalskiy Ilya S., Volkov Sergey M., Lisitsyn Alexander N., Fedorov Alexander V.

781

The need for vegetable oil is growing steadily, so increasing the volume of production. In addition, vegetable oil occupies a large segment of exports. Growth of volumes of production of vegetable oils requires new ways of management of technological processes. Fundamentally new methods of determining quality indicators of vegetable oils at all stages of production can become competitive. New opportunities are opened up by electrophysical methods. Although the methods are known for a long time, scientists come to the problem of practical implementation of the approach only in our time. This is due to the capabilities and availability of modern measuring, analyzing, computing, and software. The presented studies have used a specially designed experimental electrophysical setup and chromatograph Bruker SCION 436-GC. The relationship between the fatty acid composition of oils and the rate of change of the voltage amplitude of the signal at certain frequencies is established. The possibility of the use of electro-dynamic methods for determining quality parameters of vegetable oils as a base of a relatively inexpensive and reliable devices for production process control is justified.

DEVELOPMENT OF VISUALIZATION ALGORITHMS FOR VECTOR ELECTRONIC NAVIGATION CHARTS
Zakharov Alexey S., Tomarzhevskaya Anna S.

787

Algorithms for interpreting rules for visualization of vector electronic navigational charts that comply with international standard S101 are investigated. The advantages and disadvantages of the considered algorithms are discussed in detail. Structure of electronic charts and visualization rules, in particular classification of map objects, their properties, and methods of display are considered. A modification of the algorithm of the software interpretation of the visualization rules, which implemented their prior conversion into executable instructions is proposed. A scheme of the algorithm of pre-conversion of visualization rules is presented. The proposed modification allows to avoid additional rules processing when choosing instructions for visualization and thus to improve the software performance. Peculiarities of the proposed algorithm in comparison with the known analogues, the most important of which is the need to supply accompanying software, are described. Experimental comparison of time expenditure on visualization of electronic maps containing different numbers of objects of different types is performed. Application of the pre-conversion rules is shown to ensure a gain in performance software for the visualization of vector electronic navigational charts of more than 15 % in comparison with the algorithm of software interpretation of the visualization rules. The proposed algorithm is recommended for the use in modern navigation and information systems.

### BRIEF NOTES

BIFURCATION COMPONENT OF SLIDING FRICTION
Musalimov Victor M

793

The mechanism of dry friction is analyzed on the base of the theory of elastic stability with its successful concept of stability and critical force. Methods of the catastrophe theory are used actively to assess supercritical state of the elements of the microconstrictions with subsequent estimating the possible displacements, and the final computation of coefficients of friction. It is noted that bifurcation component of friction is desirable to be included in the list of core processes of macroscopic friction.

METHODS AND MEANS OF CONTROL OF THE DYNAMIC CHARACTERISTICS OF INERTIAL MICROMECHANICAL SENSORS AND MODULES
Gryazin Dmitry G.

797

An experience in development of complex specialized bench equipment to control frequency characteristics of the MEMS gyroscopes, accelerometers, and inertial based-on modules is described. Analyzes Peculiarities of the stands structures is analyzed, some trends in further development of stands are discussed.